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June 9th, 2015, 08:39 AM   #1
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Expected Value

Here are two Expected Value problems. Can somebody please check my answers?

1. In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets \$1 on a number and wins, then the player keeps the dollar and receives an additional \$35. Otherwise, the dollar is lost.

36 * (1/38) + -1 * (37/38)
≈ -.03

(The book says -.05. I don't understand what I did wrong)


2. A charity organization is selling \$5 raffle tickets as part of a fund-raising program. The first prize is a trip to Mexico valued at \$3450, and the second prize is a weekend spa package valued at \$750. The remaining 20 prizes are \$25 gas cards. The number of tickets sold is 6000.

3450 * (1/6000) + 750 * (1/6000) + 25 * (20/6000) + /5 (5987/6000)
≈ -4.2

Last edited by greg1313; June 10th, 2015 at 12:30 PM.
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June 10th, 2015, 12:20 PM   #2
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Quote:
Originally Posted by statssav View Post
Here are two Expected Value problems. Can somebody please check my answers?

1. In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets \$1 on a number and wins, then the player keeps the dollar and receives an additional \$35. Otherwise, the dollar is lost.

36 * (1/38) + -1 * (37/38)
≈ -.03

(The book says -.05. I don't understand what I did wrong)
If the question is "what are your expected winnings" then the answer is

$\displaystyle 35 \cdot \frac{1}{38} + (-1) \cdot \frac{37}{38} = \frac{-2}{38}$.

You don't actually win $\displaystyle \$36$. You bet $\displaystyle \$1$. That dollar is yours until you lose. If you win, you get that dollar back making everything even. Then you get your winnings of $\displaystyle \$35$.
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Last edited by greg1313; June 10th, 2015 at 12:31 PM.
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June 10th, 2015, 02:14 PM   #3
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What is the question for 2? Also what is"+ /5 (5987/6000)"?
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June 10th, 2015, 03:35 PM   #4
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I suspect that was supposed to be "-5" rather than "/5".
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June 11th, 2015, 06:20 AM   #5
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Originally Posted by mathman View Post
What is the question for 2? Also what is"+ /5 (5987/6000)"?
Yes, it is supposed to be -5. And I'm supposed to find the expected net gain to the player for one play of the game.
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June 11th, 2015, 06:33 AM   #6
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Quote:
Originally Posted by statssav View Post
1. In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets \$1 on a number and wins, then the player keeps the dollar and receives an additional \$35. Otherwise, the dollar is lost.

36 * (1/38) + -1 * (37/38)
≈ -.03

(The book says -.05. I don't understand what I did wrong)
Method #1: You pay \$1 for the spin and win \$36 if you hit the number (otherwise, you get nothing back). Expected value is 36 * 1/38 - 1 = -0.0526....

Method #2: You win \$35 if you hit the number and lose \$1 otherwise. Expected value is 35 * 1/38 + -1 * 37/38 = -0.0526....

You can see that you combined parts from these two correct methods to get an incorrect method. :(

Quote:
Originally Posted by statssav View Post
2. A charity organization is selling \$5 raffle tickets as part of a fund-raising program. The first prize is a trip to Mexico valued at \$3450, and the second prize is a weekend spa package valued at \$750. The remaining 20 prizes are \$25 gas cards. The number of tickets sold is 6000.

3450 * (1/6000) + 750 * (1/6000) + 25 * (20/6000) + /5 (5987/6000)
≈ -4.2
Not quite -- the winners still pay for their tickets. (I assume "/5" is a typo for "-5".)
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